$A\,=(6x-2)^2+(2-5x)^2+2(6x-2)(2-5x)\\\quad =(6x-2)^2+2(6x-2)(2-5x)+(2-5x)^2\\\quad =[(6x-2)+(2-5x)]^2\\\quad =(6x-2+2-5x)^2\\\quad =x^2$
Vậy $A=x^2$
$B\,=(2a^2+2a+1)(2a^2-2a+1)-(2a^2+1)^2\\\quad =[(2a^2+1)+2a][(2a^2+1)-2a]-(2a^2+1)^2\\\quad =(2a^2+1)^2-(2a)^2-(2a^2+1)^2\\\quad =-4a^2$
Vậy $B=-4a^2$
$C\,=(x+3)(x^2-3x+9)-(54+x^3)\\\quad =(x+3)(x^2-3.x+3^2)-54-x^3\\\quad =x^3+3^3-54-x^3\\\quad =27-54\\\quad =-27$
Vậy $C=-27$
$D\,=(2x+y)(4x^2-2xy+y^2)-(2x-y)(4x^2+2xy+y^2)\\\quad =(2x+y)[(2x)^2-2x.y+y^2]-(2x-y)[(2x)^2+2x.y+y^2]\\\quad =[(2x)^3+y^3]-[(2x)^3-y^3]\\\quad =8x^3+y^3-8x^3+y^3\\\quad =2y^3$
Vậy $D=2y^3$
$E\,=(a+b)^2-(a-b)^2\\\quad =[(a+b)-(a-b)][(a+b)+(a-b)]\\\quad =(a+b-a+b)(a+b+a-b)\\\quad =2b.2a\\\quad =4ab$
Vậy $E=4ab$
$F\,=(a+b)^3-(a-b)^3-2b^3\\\quad =[(a+b)^3-(a-b)^3]-2b^3\\\quad =[(a+b)-(a-b)][(a+b)^2+(a+b)(a-b)+(a-b)^2]-2b^3\\\quad =(a+b-a+b)[a^2+2ab+b^2+a^2-b^2+a^2-2ab+b^2]-2b^3\\\quad =2b(3a^2+b^2)-2b^3\\\quad =6a^2b+2b^3-2b^3\\\quad =6a^2b$
Vậy $F=6a^2b$
$P\,=(x-y)^2+(x+y)^2-2(x+y)(x-y)-4x^2\\\quad =[(x+y)^2-2(x+y)(x-y)+(x-y)^2]-4x^2\\\quad =[(x+y)-(x-y)]^2-4x^2\\\quad =(x+y-x+y)^2-4x^2\\\quad =(2y)^2-4x^2\\\quad =4y^2-4x^2$
Vậy $P=4y^2-4x^2$
